# Simultaneous Observation of Phase-Stepped Images for Photoelasticity Using Diffraction Gratings

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## Abstract

Phase-stepped photoelasticity is a powerful method for full-field stress analysis, but sequential collection of the multiple required images limits the technique to static loading applications. We have developed a system that utilizes diffraction gratings to collect four phase-stepped images simultaneously with a single camera for transient loading applications. Two adjacent, perpendicularly oriented, 1D Ronchi rulings are placed after a transparent sample to split the light into equal intensity beams for each diffraction order. The four beams that are diffracted once in the x direction and once in the y direction transmit through arrays of analyzing polariscope elements, with different combinations of fast-axis orientations for four phase-stepped images. The mirrors and imaging lenses in the system work in concert to focus each beam onto separate quadrants of the same CCD. We demonstrate the system for stress analysis of compressive loading of a Homalite-100 disk and of a Homalite-100 plate with a central hole. This system has the potential for photoelastic analysis of time-dependent materials and of dynamic events, when equipped with a high-speed camera.

## Keywords

Photoelasticity Phase-stepping Diffraction grating Stress analysis Single camera## Notes

### Acknowledgments

This work was supported by a MURI grant from the Army Research Office, grant number W911NF-07-1-0409. The authors would also like to thank the Beckman Institute for Science and Advanced Technology and the Aerospace Engineering machine shop at the University of Illinois for their assistance in this work.

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